Gently fit each crêpe, dark side up, into a buttered shallow ramekin (about 4- by 6-in. oval or 4- to 5-in. round); edges will extend over rim. Lay 1 slice prosciutto smoothly over each crêpe. Crack an egg; holding close to prosciutto, pull shell apart to let egg flow gently into 1 ramekin. Repeat step for second ramekin. Set ramekins in a 10- by 15-inch pan.
Bake in 375° regular or convection oven just until egg yolk is softly set, 8 to 10 minutes.
Meanwhile, in a 10- to 12-inch frying pan over high heat, bring about 1 inch water to a boil. Add asparagus and cook just until barely tender when pierced, 4 to 6 minutes. Drain.
Divide asparagus equally between ramekins, laying spears beside eggs. Sprinkle with cheese, and add salt and pepper to taste.